Gain insights into essential algorithms, delve into recursion, backtracking, and graph theory, and enhance your problem-solving skills in C++ to confidently tackle complex challenges.

As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem solving in C++.

Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursion, backtracking, dynamic programming, and greedy algorithms. You'll also learn about basic graph algorithms, depth-first search, shortest paths, minimum spanning trees, and all-pairs shortest paths. 

By the end of this course, you'll have acquired a wide range of skills that will significantly enhance your ability to solve problems efficiently in C++. Through this course, not only will you improve your coding skills, but you will also gain confidence in tackling complex problems.

Mastering Algorithms for Problem Solving in C++

## Characteristics of backtracking algorithms
**Backtracking algorithms** are commonly used to make a sequence of decisions, with the goal of building a recursively defined structure satisfying certain constraints. Often (but not always), this goal structure is itself a sequence. For example:

- In the $n$ queens problem, the goal is a sequence of queen positions, one in each row, such that no two queens attack each other. For each row, the algorithm decides where to place the queen.
- In the game tree problem, the goal is a sequence of legal moves, such that each move is as good as possible for the player making it. For each game state, the algorithm decides the best possible next move.
- In the $SubsetSum$ problem, the goal is a sequence of input elements that have a particular sum. For each input element, the algorithm decides whether to include it in the output sequence or not.

(Hang on, why is the goal of subset sum finding a sequence? That was a deliberate design decision. We imposed a convenient ordering on the input set by representing it using an array, as opposed to some other more amorphous data structure that we can exploit in our recursive algorithm.)

In each recursive call to the backtracking algorithm, we need to make exactly one decision, and our choice must be consistent with all previous decisions. Thus, each recursive call requires not only the portion of the input data we haven't yet processed, but also a suitable summary of the decisions we have already made. For the sake of efficiency, the summary of past decisions should be as small as possible. For example:





# Characteristics of backtracking algorithms
**Backtracking algorithms** are commonly used to make a sequence of decisions, with the goal of building a recursively defined structure satisfying certain constraints. Often (but not always), this goal structure is itself a sequence. For example:

- In the $n$ queens problem, the goal is a sequence of queen positions, one in each row, such that no two queens attack each other. For each row, the algorithm decides where to place the queen.
- In the game tree problem, the goal is a sequence of legal moves, such that each move is as good as possible for the player making it. For each game state, the algorithm decides the best possible next move.
- In the $SubsetSum$ problem, the goal is a sequence of input elements that have a particular sum. For each input element, the algorithm decides whether to include it in the output sequence or not.

(Hang on, why is the goal of subset sum finding a sequence? That was a deliberate design decision. We imposed a convenient ordering on the input set by representing it using an array, as opposed to some other more amorphous data structure that we can exploit in our recursive algorithm.)

In each recursive call to the backtracking algorithm, we need to make exactly one decision, and our choice must be consistent with all previous decisions. Thus, each recursive call requires not only the portion of the input data we haven't yet processed, but also a suitable summary of the decisions we have already made. For the sake of efficiency, the summary of past decisions should be as small as possible. For example:





Learn about common backtracking patterns, such as the implicit tree and explicit tree.

Getting Started

Introduction to Algorithm

Recursion

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

The General Pattern

Characteristics of backtracking algorithms